I know that the voltage of a cell is calculated via the Nernst Equation as $$E_\text{cell}=E^\circ-\frac{RT}{nF}\ln Q_\mathrm r$$ where $Q_\mathrm r$ represents $\frac{\text{concentration at the anode}}{\text{concentration at the cathode}}$.
However I don't understand how these concentrations actually affect the potential difference. Could anybody explain the physical processes that mean changing the concentrations affect the voltage of the cell?